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Expression of type Forall

from the theory of proveit.numbers.numerals.decimals

In [1]:
import proveit
# Automation is not needed when building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_expr # Load the stored expression as 'stored_expr'
# import Expression classes needed to build the expression
from proveit import a, n
from proveit.core_expr_types import b_1_to_n
from proveit.logic import Forall, InSet
from proveit.numbers import DecimalSequence, Digits, Natural, NaturalPos, greater, zero
In [2]:
# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [n], instance_expr = Forall(instance_param_or_params = [a, b_1_to_n], instance_expr = InSet(DecimalSequence(a, b_1_to_n), NaturalPos), domain = Digits, condition = greater(a, zero)), domain = Natural)
expr:
In [3]:
# check that the built expression is the same as the stored expression
assert expr == stored_expr
assert expr._style_id == stored_expr._style_id
print("Passed sanity check: expr matches stored_expr")
Passed sanity check: expr matches stored_expr
In [4]:
# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())
\forall_{n \in \mathbb{N}}~\left[\forall_{a, b_{1}, b_{2}, \ldots, b_{n} \in \mathbb{N}^{\leq 9}~|~a > 0}~\left(\texttt{\#}(a ~ b_{1}, b_{2}, \ldots, b_{n}) \in \mathbb{N}^+\right)\right]
In [5]:
stored_expr.style_options()
namedescriptiondefaultcurrent valuerelated methods
with_wrappingIf 'True', wrap the Expression after the parametersNoneNone/False('with_wrapping',)
condition_wrappingWrap 'before' or 'after' the condition (or None).NoneNone/False('with_wrap_after_condition', 'with_wrap_before_condition')
wrap_paramsIf 'True', wraps every two parameters AND wraps the Expression after the parametersNoneNone/False('with_params',)
justificationjustify to the 'left', 'center', or 'right' in the array cellscentercenter('with_justification',)
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Operationoperator: 7
operand: 2
1ExprTuple2
2Lambdaparameter: 35
body: 4
3ExprTuple35
4Conditionalvalue: 5
condition: 6
5Operationoperator: 7
operand: 10
6Operationoperator: 36
operands: 9
7Literal
8ExprTuple10
9ExprTuple35, 11
10Lambdaparameters: 24
body: 12
11Literal
12Conditionalvalue: 13
condition: 14
13Operationoperator: 36
operands: 15
14Operationoperator: 16
operands: 17
15ExprTuple18, 19
16Literal
17ExprTuple20, 21, 22
18Operationoperator: 23
operands: 24
19Literal
20Operationoperator: 36
operands: 25
21ExprRangelambda_map: 26
start_index: 34
end_index: 35
22Operationoperator: 27
operands: 28
23Literal
24ExprTuple32, 29
25ExprTuple32, 39
26Lambdaparameter: 42
body: 30
27Literal
28ExprTuple31, 32
29ExprRangelambda_map: 33
start_index: 34
end_index: 35
30Operationoperator: 36
operands: 37
31Literal
32Variable
33Lambdaparameter: 42
body: 38
34Literal
35Variable
36Literal
37ExprTuple38, 39
38IndexedVarvariable: 40
index: 42
39Literal
40Variable
41ExprTuple42
42Variable